Despite the specific class of model adopted to represent the continuous dynamics, a common feature of the reported approaches resides in the treatment of the switching mechanism. Indeed, the observations are typically segmented - by inferring the hidden active states - to identify the submodels, but the stochastic information behind the transitions is neither reconstruct nor exploited [1]}. In various application fields, as e.g, in the operation of industrial processes, mode transitions follows certain patterns that can be exploited to improve predictions [2]}. To this end, the discrete state evolution can be modeled by Markov chains, leading to Jump Markov Systems [3]}.
As for the piecewise and switching models above, most studies in this context have focused the linear subclasses, i.e, Jump Markov Linear Systems, jump BoxJenkins and Switched Markov AutoRegressive eXogenous systems (see e.g, [1]},[2]},[3]}). Jump Markov Nonlinear Systems are investigated in [7]}, proposing a recursive maximum likelihood approach based on a Rao-Blackwellized particle filter.
